Preheat oven to 425°F (220°C). Line a large baking sheet with parchment paper.
In a medium saucepan, bring water and 1/2 cup butter to a rolling boil over medium-high heat. Remove from heat and immediately add all the flour, stirring vigorously with a wooden spoon until a smooth ball forms.
Return the pan to medium heat and cook for 2-3 minutes, stirring constantly, until the dough dries slightly and leaves a thin film on the bottom of the pan. Transfer to a mixing bowl and let cool for 3 minutes.
Beat in the eggs one at a time with an electric mixer on medium speed, mixing until each egg is fully incorporated before adding the next. The dough should be smooth, glossy, and hold a V-shape when you lift the beaters.
Transfer dough to a piping bag fitted with a large round tip. Pipe twelve 5-inch long strips onto the prepared baking sheet, spacing them 2 inches apart. Smooth any peaks with a damp finger.
Bake for 20 minutes without opening the oven door, then reduce temperature to 350°F (175°C) and bake for 15-18 minutes more until deep golden brown and firm. Turn off oven, crack the door, and let shells dry for 10 minutes before removing.
For the custard, whisk together milk and half the sugar in a saucepan over medium heat until steaming. In a bowl, whisk egg yolks, remaining sugar, and cornstarch until smooth.
Slowly pour half the hot milk into the yolk mixture while whisking constantly, then pour everything back into the saucepan. Cook over medium heat, whisking constantly, until thickened and bubbling, about 2-3 minutes.
Remove from heat and whisk in 2 tablespoons butter and vanilla extract. Press plastic wrap directly onto the surface and refrigerate until completely cold, at least 2 hours.
For the glaze, heat heavy cream until just simmering, then pour over chopped chocolate and corn syrup. Let sit 1 minute, then stir until smooth and glossy.
Once shells are cool, use a piping bag with a small round tip to fill each éclair through three holes poked along the bottom. Dip the top of each filled éclair into the chocolate glaze and let set for 15 minutes before serving.
